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A366411 a(n) is the total number of Hamiltonian paths on rectangular grids of size n X k for 1 <= k <= n.

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%I A366411 #8 Oct 09 2023 14:01:20
%S A366411 1,5,29,353,5485,260323,15277779,3211933481,790502793321,
%T A366411 751204032996623,808973740240335345,3499358510266725179221,
%U A366411 16872857815987642169925097,333905047994165804391613820789,7308582206982080422190512432243395
%N A366411 a(n) is the total number of Hamiltonian paths on rectangular grids of size n X k for 1 <= k <= n.
%e A366411 For n = 2, the a(2) = 5 solutions are:
%e A366411   +---+  +---+---+  +---+---+  +---+---+  +---+---+
%e A366411   |   |  |   |   |  |   |   |  |   |   |  |   |   |
%e A366411   | * |  | **|** |  | * | * |  | **|** |  | **|** |
%e A366411   | * |  |   | * |  | * | * |  | * |   |  | * | * |
%e A366411   +---+  +---+---+  +---+---+  +---+---+  +---+---+
%e A366411   | * |  |   | * |  | * | * |  | * |   |  | * | * |
%e A366411   | * |  | **|** |  | **|** |  | **|** |  | * | * |
%e A366411   |   |  |   |   |  |   |   |  |   |   |  |   |   |
%e A366411   +---+  +---+---+  +---+---+  +---+---+  +---+---+
%Y A366411 Row sums of triangle A366399.
%K A366411 nonn,walk,more
%O A366411 1,2
%A A366411 _Douglas Boffey_, Oct 09 2023
%E A366411 More terms (using A332307) from _Pontus von Brömssen_, Oct 09 2023